دانلود کتاب Musica Mathematica: Traditions and Innovations in Contemporary Music

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Cover
Contents
List of Analyzed Music Scores
Author’s Preface
Foreword: Mathesis as a Philosophy of the Beauty of Music
Part 1 A Retrospective of the Traditions of Musica Mathematica
1. The Constructive Relationships between Music and Mathematics: The Pythagorean Conception of Universal Music and its Spread in the Worldview of Later Periods
1.1. Music and the Theory of the Quadrivium
1.2. Review of the Harmony of Spheres
1.3. The Phenomenon of Mathesis Universalis
1.4. Expression of Numerical Proportions and Progressions
The Fibonacci Progression and the Golden Ratio Phenomenon
1.5. Ars Combinatoria and the Constructivism of Music
2. Semantic Interpretation of the Interaction between Music and Mathematics: Mystic Middle Ages and the Sacral Baroque
2.1. Semantics of the Kabbalah in Music
2.2. Symbolic Thinking and Sacral Numerology
2.3. Codes of the Numerical Alphabets in Music
3. Constructive Aspects of the Interaction between Music and other Arts
3.1. “Frozen Music”: Dialogues between Music and Architecture
3.2. Ut Pictura Musica: The Interaction between Music and Art
3.3. Musical Cryptography as a Common Denominator of the Sound and the Word
Application of the Morse Alphabet
4. Musica Mathematica in Practice: Aspects of Analysis
Part 2 The Renewal of Mathematical Techniques in Musical Compositions of the 20th and 21st Centuries
1. Constructive Aspects of Music Composition
1.1. The Implications of Numerical Proportions and Progressions in Music
1.1.1. The Number Proportions and Progressions of Antiquity
Olivier Messiaen. Quatre études de rythme (1949–1950)
Snieguolė Dikčiūtė. The Mystery of Seven Bridges (1991)
Steve Reich. Music for Pieces of Wood (1973)
Siegfried Thiele. Proportionen (1971)
John Cage. First Construction (1939)
1.1.2. Fibonacci and Number Sequences Derived from it
Derek Bourgeois. Symphony for Organ, Op. 48 (1975)
Steve Reich. Clapping Music (1972)
Karlheinz Stockhausen. Klavierstück IX (1961)
1.1.3. The Prime Numbers and other Mathematically Determined Sequences
Alain Louvier. L’Isola dei Numeri (1991)
Tom Johnson. Music for 88 (1988)
1.2. The Renewal of Polytempo, Polyrhythm, and Polymeter
John Adams. Short Ride in a Fast Machine (1986)
Conlon Nancarrow. Study for Player Piano No. 15 (premiere in 1962)
György Ligeti. Désordre (1985)
1.3. Symmetrical Algorithms and the Confrontation between Symmetries and Asymmetries
Morton Feldman. Crippled Symmetry (1983)
1.4. Transformational Elements (Combinatorics, Permutations, Rotations)
Olivier Messiaen. Île de feu II (1950)
Tom Johnson. Tango (1984)
Tom Johnson. The Chord Catalogue (1986)
2. Semantic Aspects of Music Composition
2.1. Cosmological Number Codes and Graphic Constructions
2.2. The Symbols of Magic Number Squares
Šarūnas Nakas. Ziqquratu (1998)
Dmitri Smirnov. Two Magic Squares (1971)
2.3. The Implications of Sacred Numbers
Bronius Kutavičius. The Gates of Jerusalem (1991–5)
Snieguolė Dikčiūtė. The Mystery of the Seven Bridges (1991)
2.4. Personalized Semantics: The Significance of Individual Numbers
George Crumb. Black Angels (1970)
John Cage. Ryoanji (1983)
Mikalojus Konstantinas Čiurlionis. Fugue in B-flat, Op. 34/VL 345 (1908–9)
Part 3 Innovations of Mathematical Techniques in 20th and 21st Century Music
1. The Mathematized Musical Graph
1.1. A Geometric Prototype as an Algorithm for Musical Composition
Jan Rokus van Roosendael. Rotations (1988)
John Adams. China Gates (1977)
1.2. L-system Formalities in Music
Tom Johnson. Piece No. 14 from the cycle Rational Melodies (1981)
Gary Lee Nelson. Summer Song (1991)
1.3. The Numericalization of the Musical Score
Morton Feldman. IXION (1958)
2. Implications of Modern Mathematical Theories
2.1. The Practice of Algorithmic Music and Computer-Generated Composition
2.2. Tonal Adaptations of Complicated Mathematical Processes
Iannis Xenakis. Nomos alpha (1965)
2.3. Fractal Theory Analogies in Musical Compositions
Šarūnas Nakas. Ziqquratu (1998)
Vytautas V. Jurgutis. Fractals (1999)
Charles Dodge. A Fractal for Wiley Hitchcock (1989)
Afterword
Bibliography
Supplementary Literature on the Subject of this Book
Index of Names
About the Author